Bayesian estimation of the Pareto model based on type-II censoring data by employing non-linear programming

The main goal of this article is to determine the optimally weighted coefficients (omega 1and omega 2) of the balanced loss function of the form. L Kappa,omega , xi o (psi(sigma), xi) = omega 1 gamma(sigma)Kappa(xi o, xi) + omega 2 gamma(sigma) Kappa(psi(sigma), xi); omega 1 + omega 2 = 1 . Based on Type II Censored Data, by applying non-linear programming to estimate the shape parameter and some survival time characteristics, such as reliability and hazard functions of the Pareto distribution. Considering two balanced loss functions (BLF), including balanced square error loss function (BSELF) and balanced linear exponential loss function (BLLF), the calculation is based on the balanced loss function, including symmetric and asymmetric loss functions, as a special case. Use Monte Carlo simulation to pass Bayesian and maximum likelihood estimators through. The results of the simulation showed that the proposed model BLLF has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than the corresponding loss function.